3 Answers

It really depends on your team. Honestly. You need to determine your synergy and team role first, as they both have different, and sometimes, similar roles.

Nidoqueen:

Nidoqueen is quite concrete in RU, being to fill roles such as Special sweeper, hazard setter, wall, and Status absorber. First off, allow us to look at its stats.

90 HP / 82 Atk / 87 Def / 75 SAtk / 85 SDef / 76 Spd
495 BST

Those stats seem extremely mediocre, don't they? Well, Nidoqueen's mediocre stats gives it rather decent bulk, but that speed stat blows. That Special Attack stat can be patched up rather easily. It is able to run a simple Life Orb set with 4 moves with beneficial side effect attacks to nab both Sheer Force and an LO boost with no recoil whatsoever. Nidoqueen is extremely powerful in this regard. After both boosts, it essentially has a 461 Special Attack stat. Combined with her neutral coverage in the RU tier, Nidoqueen is a forced to reckoned with. One can also use Nidoqueen to absorb status, as it is both immune to Thunder Wave and Toxic, two common status moves in the UU tier. Furthermore, Nidoqueen has access to Stealth Rock and Toxic Spikes, allow her to utilize her decent defensive stats to absorb Toxic Spikes that the opponent set up, and then set her own.

Drapion:

Drapion shares some similar roles with Nidoqueen, that's for sure. Take a look at its stats, for one:

70 HP / 90 Atk / 110 Def / 60 SAtk / 75 SDef / 95 Spd
500 BST

These stats seem better compared to Nidoqueen, for sure. It can effectively set up Toxic Spikes like Nidoqueen, but lacks Stealth Rock. The newest addition to RU, Amoonguss, and many of the Poison type Pokemon in RU, often come in to absorb them anyway, so they're not as useful as usual. Drapion can also phaze with Whirlwind. While Nidoqueen could have also done so herself with Roar or Dragon Tail, but Drapion's decent mixed bulk allows it to take hits way better. Also, Drapion also has access to Taunt, allowing it to shut down many of the status moves of RU. Furthermore, Drapion can run a Attacking stat with Swords Dance, and with base 90 Atk and 95 Spd, it will be doing some hefty damage. This guy also has access to Pursuit, allowing it to trap Ghosts and, in most cases, KOing them. Finally, Drapion has less weaknesses, allowing for better synergy. However, Nidoqueen offers more resistances.

Let's start with Nidoqueen.
Four weaknesses. We're already off to a bad start.
Really good movepool. I mean REALLY good.

Drapion:
One weakness. Ground, easy to defend against.
His ability, sniper, paired with scope lens leads to some awesome OHKO. You can also give him increased critical hit moves, like cross poison and night slash.
Movepool isn't nearly so good as Nidoqueen, but...

I have used Drapion and I love him. A great Pokemon to use, especially with his sniper ability. His defenses aren't as good as Nidoqueen but that's an easy fix with EV training.

Nidoqueen and Nidoking are two Pokemon I hate and will never again battle with. I guarentee that every second Pokemon you fight with it has a move that is supereffective against it.

Scope Lenses are banned in competitive, and he wants it for competitive. Nidoqueen has nice defenses, a great movepool, SHEER FORCE, again, a great movepool to compliment his ability, and is a Special attacker. You can't compare the two. You're denying that Nidoqueen is good because you hate it.

in my opinion nidoqueen is a lot better but both have a different role because one is a special attacker but ones a physical attacker. nidoqueen has an amazing movepool with earth power, fire blast, ice beam, sludge wave, thunderbolt, focus blast, and many more. also these moves are powered up by sheer force so with a life orb nidoqueen has a lot more special attack than it seems!!! people cant really do much when everything they can switch in is ohkod by the right move so shes really dangerious.

drapion is a physical attacker though, he has better speed so things like feraligator cant revenge kill him. however hes alot weaker and doesnt have as good coverage so hes easier to wall. especially sandslash since thats used a lot (even tho its not very good tbh).

i'd go with niduqueen usually if you want a wallbreaker or hard hitter. however drapions great typing and moves like swords dance, taunt and pursuit make him alot better at killing pesky psychics or ghosts. hope I helped you out :D